Question

please help guys. want complete solution​

Answer 1

Solution :-

Given

→ (x + 3)² + |x + 3| - 6 = 0

Let "x + 3" = t

→ t² + |t| - 6 = 0

Now when

t ≥ 0

→ t² + t - 6 = 0

→ t² + 3t - 2t - 6 = 0

→ t(t + 3) - 2(t + 3)

→ (t + 3)(t - 2)

→ t = -3 , 2

or as t ≥ 0

→ t = 2

t < 0

→ t² - t - 6 = 0

→ t² - 3t + 2t - 6 = 0

→ t(t - 3) + 2(t - 3)

→ (t - 3)(t + 2)

→ t = -2 , 3

or as t < 0

→ t = -2

So either

t = +2

or

t = -2

Then

→ ( x + 3) = 2

→ x = 2 - 3

→ x = -1

or

→ (x + 3) = -2

→ x = -2 - 3

→ x = -5

So

x = -5 , -1

Or sum of real roots

= -5 + (-1)

= -6

Answer 2

$\huge{\textbf{\underline{Answer:-}}}$

Given:-

→ (x + 3)² + |x + 3| - 6 = 0

Let x + 3 = t

→ t² + |t| - 6 = 0

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$\huge{\textbf{\underline{Explanation:-}}}$

Now when

t ≥ 0

→ t² + t - 6 = 0

→ t² + 3t - 2t - 6 = 0

→ t(t + 3) - 2(t + 3)

→ (t + 3)(t - 2)

→ t = -3 , 2

or as t ≥ 0

→ t = 2

Now when

t < 0

→ t² - t - 6 = 0

→ t² - 3t + 2t - 6 = 0

→ t(t - 3) + 2(t - 3)

→ (t - 3)(t + 2)

→ t = -2 , 3

or as t < 0

→ t = -2

So,

t = +2

or

t = -2

Then

→ ( x + 3) = 2

→ x = 2 - 3

→ x = -1

or

→ (x + 3) = -2

→ x = -2 - 3

→ x = -5

So

x = -5 , -1

Or sum of real roots

= -5 + (-1)

= -6

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